pathfinder-1e – Do Eidolons Gain Levels and Feats?

The approximate assumed wealth by level for a seventh level character is 23,500 gp, so you could afford such an item but it would account for half your wealth. Of course, specific campaigns vary, and if you have a party crafter you can halve the cost to you. And youe WBL about doubles every two levels so probably by level 9 it's more affordable, if it's a major part of your build.

No, eidolon levels do not stack in any way with animal companion levels.

An eidolon is not an animal companion so cannot benefit from Pack Flanking in any event.

However, I suspect you should probably be asking instead what your actual problem is - unless one or both of you have a lot of rogue levels, there's perhaps other better ways to reap a +2 to hit on your opponent, you have mentioned no real reason that you need flanking specifically. For flanking you could possibly use Gang Up instead, with another party member or, you know, a summon.

1. Any 2 claws. Nothing anywhere says different, just that it requires two claw hits.

2. Only once per round. The wording you quoted doesn't specify "for each two successful claw attacks...", just when it gets two. The additional claws just make it easier to proc (and do their own damage, of course). Notably, however, unlike normal rend, the wording for Unchained Eidolon's rend evolution seems to leave it open for getting one rend per round per target. I would probably rule against that in my own games, but it's certainly a valid interpretation of the wording.

3. It is not, as I answered here. Rend is applied as bonus damage to the second successful claw attack, not as a separate attack, so it doesn't gain the benefit of (or take the penalty for) per-attack effects. This includes Power Attack, flaming, or any Damage Resistance the target has, making rend a useful way to punch through DR.

4. No, again, because it's not a separate attack. That damage is already applied as part of the claw that's getting the bonus rend damage.

5. The wording on that ability seems to leave that option open as well. Even a "half-and-half" approach should work, where if you hit the target during your full attack and then hit it again before your next turn with an AoO or immediate action, the second claw should get the rend damage. That's still going to be a bit of a GM call, and will probably be ruled the same way as the "once per round per target" option from part 2, since they rely on the same interpretation of that wording.

P.S. re #5: Running through a creature's threatened area only provokes one AoO from that creature, regardless of the number of their threatened squares you run through. Just an aside, since the question implies you'd get multiple free shots in that situation.